Fraction Review

10 Questions

What is the numerator in a fraction?

The top number

What is the main rule to simplify a fraction?

Divide both the numerator and denominator by the largest number that will divide evenly into both

What is the result of multiplying two fractions?

The product of the numerators and the product of the denominators

What does it mean for a fraction to be simplified?

The numerator and denominator have no factors in common other than 1

What is the purpose of simplifying fractions?

To make the fraction easier to work with

What is the correct method to multiply fractions?

Multiply the first fraction by the reciprocal of the second fraction

What is the requirement for adding or subtracting fractions?

Denominators must be the same

What is the result of multiplying $2/3$ and $5/7$?

10/21

What is the result of adding $3/5$ and $2/5$?

5/5

What is the result of subtracting $3/7$ from $5/7$?

2/7

Study Notes

Fraction Basics

A fraction consists of two numbers: a numerator (the top number) and a denominator (the bottom number).
Numerator represents the number of parts, while denominator represents the number of parts that make a whole.

Simplifying Fractions

A fraction is simplified if the numerator and denominator have no factors in common other than 1.
To simplify a fraction, divide both the numerator and denominator by the largest number that will divide evenly into both.

Examples of Simplified Fractions

16/60 = 1/6
75/120 = 5/8
7/18 = 7/18
10xy/15y = 2x/3y
5/15 = 1/3
13/26 = 1/2

Multiplying Fractions

Multiply straight across, numerator times numerator and denominator times denominator.
Simplify, if possible.

Examples of Multiplying Fractions

3/1 × 4/5 = 12/5
11/3y × 3/5y = 33y/15y
2/5 × 5/5 = 2/5
9a/2 × 10/5 = 9a/1

Dividing Fractions

Multiply the first fraction by the reciprocal (flip) of the second fraction.

Examples of Dividing Fractions

2/5 ÷ 3/1 = 2/5 × 1/3 = 2/15
3y/5y ÷ 6y/3y = 3y/5y × 3y/6y = 1/2
7/x ÷ 2/5 = 7/x × 5/2 = 35/2x

Adding or Subtracting Fractions

DENOMINATORS must be the SAME to add or subtract fractions.
Get a common denominator, if needed, then add or subtract the numerators and keep the common denominator.
Simplify, if possible.